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In topology, the wedge sum is a "one-point union" of a family of topological spaces. Specifically, if X and Y are pointed spaces the wedge sum of X and Y is the quotient space of the disjoint union of X and Y by the identification x 0 ∼ y 0 : {\displaystyle x_{0}\sim y_{0}:}
where ∼ {\displaystyle \,\sim \,} is the equivalence closure of the relation { } . {\displaystyle \left\{\left\right\}.} More generally, suppose i ∈ I {\displaystyle \left_{i\in I}} is a indexed family of pointed spaces with basepoints i ∈ I . {\displaystyle \left_{i\in I}.} The wedge sum of the family is given by:
The wedge sum is again a pointed space, and the binary operation is associative and commutative.
Sometimes the wedge sum is called the wedge product, but this is not the same concept as the exterior product, which is also often called the wedge product.